École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Nonlinear system. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Azo-azulene derivatives as second-order nonlinear optical chromophores

Abstract: The molecular and solid state nonlinear optical (NLO) properties of several (phenylazo)-azulenes are investigated. In particular, (4-nitrophenylazo)-azulene (2 b) exhibits a quadratic hyperpolarizability (βvec) of 80×10−30 cm5 esu recorded at 1.907 μm by the electric field-induced second-harmonic (EFISH) technique. This molecular material, which crystallizes in the monoclinic noncentrosymmetric space group Pc, exhibits an efficiency 420 times that of urea in second-harmonic generation. The origin of the optical nonlinearity in azo-azulene is discussed in relation with crystal structures and semiempirical calculations within the INDO/SOS formalism, and compared with that of the well known disperse red one (DR1) organic dye.

On the Entropic Structure of Reaction-Cross Diffusion Systems

Abstract: This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the cross diffusions is convex, while the other one is concave. The treatment of such cases involves a general study of the structure of Lyapunov functionals for cross diffusion systems, and the introduction of a new scheme of approximation, which provides simplified proofs of existence.

Structure of shape derivatives

Abstract: In this paper, we describe the precise structure of second "shape derivatives", that is derivatives of functions whose argument is a variable subset of \( \mathbb{R}^N \). This is done for Frechet derivatives in adequate Banach spaces. Besides the structure itself, interest lies in the way it is derived: the starting point is a "functional analytic" statement of the well-known fact that small regular perturbations of a given regular domain may be "uniquely" represented through normal deformations of the boundary of this domain. The approach involves the implicit function theorem in a convenient functional space. A consequence of this "normal representation" property is that any shape functional may be described through a functional depending on functions defined only on the boundary of the given domain. Differentiating twice this representation leads to the structure theorem. We recover the fact that, at critical shapes, the second derivative around the given domain depends only on the normal component of the deformation vector-field at its boundary. Some examples are explicitly computed.